Fatigue of Top Chain
of Mooring Lines due to
In-plane and Out-of-plane Bendings
October 2014
Guidance Note
NI 604 DT R00 E
Marine & Offshore Division
92571 Neuilly sur Seine Cedex – France
Tel: + 33 (0)1 55 24 70 00 – Fax: + 33 (0)1 55 24 70 25
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BV Mod. Ad. ME 545 L - 7 January 2013
GUIDANCE NOTE NI 604
Fatigue of Top Chain of Mooring Lines due to
In-plane and Out-of-plane Bendings
SECTION 1
GENERAL
SECTION 2
MOORING ANALYSES FOR COMBINED FATIGUE ESTIMATION
SECTION 3
COMBINED FATIGUE ESTIMATION
APPENDIX 1
ALTERNATIVE DESIGN REQUIREMENTS
October 2014
Section 1
General
1
Scope
1.1
2
Application
Definition
2.1
3
5
5
Top chain combined fatigue
References
5
3.1
4
Methodology
4.1
Section 2
Methodology for analysis
1.1
1.2
2
10
Global line assessment
Local line assessment
Requirements for mooring analysis
2.1
2.2
2.3
12
Mooring Analysis Method
Selection of design conditions
Sensitivity on loading conditions and mooring system model
Combined Fatigue Estimation
1
General
1.1
2
3
15
Bending moment threshold
Stiffness variability
Static OPB/IPB moments evaluation
16
Stress concentration factor estimation
Corrosion effect
Stresses combination
Design fatigue damage calculation
5.1
5.2
5.3
14
Tests on full scale chains
Results from other tests
Interlink stiffness from full scale tests
Combined stress estimation
4.1
4.2
4.3
5
General
Evaluation of bending moments
3.1
3.2
3.3
4
14
Definition of interlink stiffness
2.1
2.2
2.3
2
General methodology
Mooring Analyses for Combined Fatigue Estimation
1
Section 3
6
18
SN-curve
Fatigue damage calculation
Design criteria
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October 2014
Appendix 1 Alternative Design Requirements
1
General
1.1
2
Tension-tension, in-plane bending and out-of-plane bending modes
Evaluation of stresses in mooring line
2.1
2.2
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20
20
OPB and IPB stiffness and moments
OPB and IPB stresses
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3
4
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October 2014
NI 604, Sec 1
SECTION 1
1
1.1
GENERAL
Scope
Application
1.1.1 The present Guidance Note provides the methodologies, requirements and recommendations to be considered
in the evaluation of top chain combined fatigue under tension loading, in-plane bending loading and out-of-plane
bending loading for the classification of permanently
moored offshore units.
1.1.2 In the present Guidance Note, the top chain corresponds to the 20 first chain links of the mooring line after
fairlead chain stopper.
1.1.3 The requirements of the present Guidance Note are
complementary to provisions of Rule Notes listed in [3.1.1]
for granting the POSA notation to permanent offshore floating units.
1.1.4 The evaluation of combined fatigue at top chain connection is to be performed when the pretension in mooring
lines at intermediate draft is higher than 10% of the Minimum breaking strength of a chain of the same diameter in
Oil Rig Quality (ORQ) grade and when the design life on
site is higher than 2 years.
2
2.1
Definition
Top chain combined fatigue
2.1.1 Loadings in Top chain
Chains in mooring lines are designed to resist tension loads
in line with chain direction. Far from connection points, the
angular variation between two chain links is negligible and
the assumption of pure tension loading is valid. However, at
connection points such as chain stoppers, when one link is
forced to rotate with regards to the adjacent link, higher
bending moments are imposed in the first following links,
generating additional fatigue damage.
At fairlead/chain-stopper location, the motions and rotations of the vessel are imposed to the fairlead and the link
retained in fairlead pocket whereas the motions of the
mooring lines, following mooring line catenary, are
imposed to the adjacent chain links.
Due to the angular differences between fairlead and chain
and to friction between links, high bending moments are
imposed to the first links of the top chain.
2.1.2 Chain bending modes
Roll between chain links is largely prevented by the chain
proofloading during fabrication (imprint of a pocket at contact area between links).
October 2014
Between two links, the following two main behaviours in
bending can thus develop:
• A sticking mode: static friction mode where adjacent
links behave as locked.
• A sliding mode: dynamic friction mode when interlink
moment is exceeding friction limit.
The different behaviours define a non-linear interlink stiffness.
2.1.3
In-plane and out-of-plane bending of top chains
Three different bending modes can be defined depending
on the direction of the bending moment:
• An in-plane bending (IPB) mode where the link is bent
within its main symmetry plane.
• An out-of-plane bending (OPB) mode where the link is
bent out of its main plane.
• A torsional mode where the link is in torsion around its
main axis. This mode can generally be neglected for
combined fatigue evaluation in the top chain.
The interlink stiffness naturally relates two adjacent links
whose plane are at right angles.
2.1.4 Combined stresses in top chain
Three loadings of the chain and resulting stresses are thus to
be defined:
• Tension-tension (TT) loading due to axial tension loads
in the link.
• In-plane bending (IPB) loadings due to bending in the
main plane of the link.
• Out-of-plane bending (OPB) loadings due to bending
out of the main plane of the link.
The loading of the chain can be decomposed within these
three types of loading and the resulting stresses are to be
combined in order to obtain the total stress for fatigue damage evaluation.
3
References
3.1
3.1.1 Rule Notes
• NR445, Rules for the Classification of Offshore Units
• NR493, Classification of Mooring Systems for Permanent Offshore Units
• NR494, Rules for the Classification of Offshore Loading
and Offloading Buoy.
3.1.2 Other reference documents
• OTC 17238
Failure of Chains by Bending on Deepwater Mooring
Systems, P.Jean, K.Goessens, D.L’Hostis, Offshore Technology conference, May 2005
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5
NI 604, Sec 1
• OMAE 67353
Out-of-Plane Bending Testing of Chain Links, C.Melis,
P.Jean, P.Vargas, International Conference on Offshore
Mechanics and Arctic Engineering, June 2005
• RR-M-86-007
Chain Out of Plane Bending - JIP Report, L.Rampi, May
2013.
4
Methodology
• OMAE 67354
FEA of Out-of-Plane Fatigue Mechanism of Chain Links,
P.Jean, P.Vargas, International Conference on Offshore
Mechanics and Arctic Engineering, June 2005
• OMAE 92488
Fatigue Testing of Out-of-Plane Bending Mechanism of
Chain Links, L.Rampi, P.Vargas, International Conference on Offshore Mechanics and Arctic Engineering,
June 2006
4.1
General methodology
4.1.1 The methodology for OPB calculation methodology
can be divided into 3 steps:
• fatigue mooring simulations
• interlink stiffness computation
• fatigue damage evaluation.
Details of the methodology are presented in the following
graphs.
Figure 1 : General methodology
Fatigue mooring analysis providing:
- Time series of tensions and angles at fairlead
for damage calculation
- Maximum angles and tensions at fairlead to be
considered for OPB/IPB interlink stiffness analysis
Details of mooring analysis in Fig 2 and Sec 2
OPB/IPB interlink stiffness analysis providing relationship
for damage computation between:
- Chain angles at fairlead
- Tension at fairlead
- OPB/IPB interlink moments for the first two links
of the chain
- OPB/IPB interlink angles for the first two links of
the chain
Details of stiffness analysis in Fig 3 and Sec 3
Combined top chain fatigue damage computation in time domain
Details of combined damage computation in Fig 4 and Sec 3
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NI 604, Sec 1
Figure 2 : Methodology for mooring analysis and post processing
Mooring pattern
Hydrodynamic database
Meteocean data:
Scatter diagram or hindcast data
or in situe measurement
See NR 493
See NR 493
See NR 493
Fatigue mooring analysis in time domain for each Sea State
(SS) from metocean data and for each mooring line i
See NR 493 and Sec 2, [1.1] & Sec 2, [2]
Time series of tension
at fairlead Ti,SS(t)
See Sec 2, [1.1.3]
Time series of top chain
angle in the plane of
the line 1,i,SS(t)
See Sec 2, [1.1.3]
Time series of top chain
angle out of the plane
of the line 2,i,SS(t)
Time series of vessel /
turntable rotations at fairlead
connection local axis
See Sec 2, [1.1.3]
1,i,SS(t) and
2,i,SS(t)
See Sec 2, [1.1.3]
Calculation of the time series of moment at fairlead in the plane of
the line M1,i,SS(t) and out of the plane of the line M 2,i,SS(t)
considering no rotation of the fairlead

See Sec 2, [1.2]
Tracking of the effective moment in the fairlead in the plane
M1,i,SS(t) and out of the plane of the line M2,i,SS(t)
considering no rotation of the fairlead considering
the friction limits of the fairlead
See Sec 2, [1.2.2] & Sec 2, [1.2.3]
Fairlead bushing
limit friction
See Sec 2, [1.2.4] &
Sec 2, [1.2.5]
Calculation of the angle the fairlead w.r.t. the vessel
moment in the plane 1,i,SS(t) and
out of the plane of the line 2,i,SS(t)
See NR 493 and Sec 2, [1.2.2] & Sec 2, [1.2.3]
Minimum and maximum
tension at fairlead for all
the seastates and lines
Tmin and Tmax
Calculation of the actual angle of the fairlead
in the plane 1,i,SS(t) and out of the plane
of the line 1,i,SS(t)
See Sec 2, [1.2.2]
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Minimum and maximum
angle at fairlead for all
the seastates and lines
1,min, 1,max
2,min, and 2,max
7
NI 604, Sec 1
Figure 3 : Methodology for OPB/IPB interlink stiffness analysis
Results of static tests OPB/IPB
tests providing interlink stiffness
function of:
- Tension
- Interlink angle int
- Variability of stiffness
Minimum and maximum
tension at fairlead for all
the sea states and lines
Tmin and Tmax
Minimum and maximum
angle at fairlead for all
the sea states and lines
1,min’
and
1,max’
2,min
2,max
See Sec 3, [2.1] & Sec 3, [2.2] &
Sec 3, [2.3.3] & Sec 3, [3.2] and
App 1, [2.1]
Implementation of a FEM beam model or a non-linear stiffness model
of the top chain of the mooring line considering:
- Each mooring link as a single beam
- A load point at fairlead connection imposing tension and angle in the first
beam
- A pinned boundary connection at the end of the line model
- Actual link axial, in plane and out of plane stiffness on each beam
- Interlink stiffness between the beams for in plane bending of the link and
out of plane bending of the link
See Sec 3, [3.3.1] & Sec 3, [3.3.2]
Loading of the beam model with every possible combination of:
- Tension at fairlead between Tmin and Tmax
- Angles at fairlead in the plane of the line between
1,min
and
1,max
or out of the plane of the line between 2,min and 2,max
See Sec 3, [3.3.2]
Evaluation for each link j in the line i and for each combination of tension and
angle of:
- The interlink angle in the plane of the link int/IPB,i,j(T,
)
1’ 2
int/OPB,i,j(T, 1’ 2)
- The interlink moment in the plane of the link MIPB,i,j(T,
)
1’ 2
- The interlink angle out of the plane of the link
- The interlink moment out of the plane of the link MOPB,i,j(T,
1’ 2
)
See Sec 3, [3.3.2]
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Figure 4 : Methodology for damage computation
Time series of tension at
fairlead Ti,SS (t) for the
line i and seastate SS
Time series of angles of
the fairlead in the fairlead
in the plane 1,i,SS (t) and
out of the plane of the
line 2,i,SS (t) in the line i
The relation between tension,
fairlead angles w.r.t line and:
- Interlink moment in the plane
MIPB,i,j (T, , )
1 2
- Interlink moment out of the
plane of the link
MOPB,i,j (T, , )
1
2
Time series of interlink moment in the plane of the
link MIPB,j,i (t) and out of plane of the link MOPB,j,i (t)
for the link j in the line i
See Sec 3, [3.3.3]
Time series of nominal
TT stress TT,i,SS (t)
Time series of nominal
OPB stress OPB,i,jSS (t)
for each line i and link j
Time series of nominal
IPB stress IPB,i,jSS (t)
for each line i and link j
Application of SCF for each hot spot considering:
- Diameter effects
- Pretension effects
Combination of TT, OPB and IPB stresses as per Sec 3, [4]
Apply rainflow counting to obtain long term distribution of
stresses. Use appropriate SN curve to derive damage
See Sec 3, [5]
Verification of the safety factor against acceptance criteria
See Sec 3, [5.3]
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NI 604, Sec 2
SECTION 2
MOORING ANALYSES FOR COMBINED FATIGUE
ESTIMATION
Symbols
T
P
: Tension in the line at top chain attachment point
: Pretension in the line at top chain attachment
point, for the simulated condition
α1, α2 : Chain angle at connection considering a perfectly pinned connection in fairlead global axis
β1, β2
: Vessel rotation in fairlead global axis
δ1, δ2
: Fairlead rotations in fairlead global axis
γ1, γ2
: Relative chain angle at fairlead
γTT
: Mean stress correction factor on multiaxial OPB
SCF
μ
: Friction coefficient between steel and steel
αint
: Interlink angle between the considered link and
the next adjacent link
d
: Chain diameter
D
: Total fatigue damage
Di
: Elementary fatigue damage
D-DAF : Dynamic Damage Amplification Factor
FCS
: Fairlead - Chain stopper
FEM
: Finite Element Methods
TT
: Tension-Tension loading
IPB
: In-plane bending of chain
OPB
: Out-of-plane bending of chain
MOPB
: Moment in chain at interlink contact area in
OPB direction
MIPB
: Moment in chain at interlink contact area in IPB
direction.
Time series of chain angles and tensions at fairlead are to be
provided for each metocean and loading conditions. These
time series are to be post processed in order to obtain time
series of relative chain angles in the plane and out of the
plane of the fairlead, following the methodology defined in
[1.2].
1
These chain and vessel angular motions are to be transposed in the FCS local axis, defining angles within the horizontal axis of the FCS (α1,β1,δ1) and vertical axis of the FCS
(α2,β2,δ2).
1.1
Methodology for analysis
Global line assessment
1.1.1 In order to assess combined fatigue of top chains at
attachment points, the global line behaviour is to be
assessed through dedicated mooring analyses considering
detailed modelling of the vessel motions, of the line tension, of the angles between chain and fairlead at attachment
point.
Interlink moments and combined stresses for fatigue evaluation are to be obtained through post-processing of these
time series as defined in Sec 3.
1.1.4 Alternative methodologies will be given consideration, on a case by case basis, provided they demonstrate to
provide a Safety Level equivalent to that resulting from the
application of the present document.
1.2
Local line assessment
1.2.1 Chain relative angle assessment
Relative angle between chain and fairlead-chain stopper
(FCS) is driven by chain motions, vessel motions and fairlead characteristics.
The angular motions on the chain and of the vessel are to be
transposed in the FCS local axis system at chain connection,
considering the abilities of rotation of the FCS.
Chain angle α is considered as the angle at chain connection when considering a perfectly pinned joint connection
of the chain on the vessel at FCS connection in global axis.
The vessel rotations β and the angle between FCS and vessel δ are to be considered in the global axis.
The relative chain angle γ at fairlead is then expressed as
following, limited by FCS sliding abilities (see [1.2.2]):
γ1 = β1 + δ1 − α1
γ2 = β2 + δ2 − α2
1.1.2 The analyses methodology adopted for combined
fatigue evaluation is to be in line with the provisions of
NR493 Rules for the Classification of Mooring Systems for
Permanent Offshore Units.
1.2.2 FCS rotations behaviour
Most modern FCS have rotation abilities around vertical and
horizontal axes in order to reduce bending moments in
mooring line top chains, so the angle between vessel and
FCS is not constant.
1.1.3 Lines tensions and angles at attachment points are to
be assessed through time-domain methodologies.
A pinned boundary condition of the chains at fairlead are to
be considered.
These rotation abilities are limited by friction phenomena in
bushings of axes of FCS, generating sliding limits of FCS
axes under which the fairlead rotation is prevented, inducing bending fatigue of chain.
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NI 604, Sec 2
Figure 1 : Chain relative angles at FCS
Vessel
FCS
End of FCS the time
series of motions are
to be provided
Chain
This limiting moment is to be thoroughly investigated
through testing. A sliding behaviour of the FCS as close as
possible to effective fairlead behaviour is to be implemented in relative angle assessment.
The limiting moment can also be evaluated as a break-out
angle above which the fairlead chain stopper starts sliding
(see Fig 2).
Figure 2 : Sticking/sliding behaviour of the FCS
• a sliding mode: when the moment tends to be higher
than the limiting moment, the angle δ varies in order to
keep the moment at limiting value.
Simplified methodologies such as truncated angle time
series are generally not allowed, except if demonstrated to
provide a Safety Level equivalent to that resulting from the
application of the present document.
1.2.4
Break out angle
Functional tests of FCS
Sticking/sliding behaviour of FCS is to be tested on full scale
prototypes against imposed rotations of the FCS under fixed
axial loads, unless the approach in [1.2.5] is followed. Testing is to be performed in seawater for submerged FCS.
Sliding limit
in angle
The range of axial loads in tests is to be in accordance with
maximum and minimum loads seen in fatigue mooring simulation time series.
The upper bound relation between load and limiting
moment is to be assessed for the evaluation of FCS rotations.
Sliding limit
in angle
The static friction coefficient of the bushing material is to be
measured on the prototype.
1.2.5
Angle between vessel and fairlead
Angle between chain and fairlead
End of sliding of fairlead
1.2.3
Evaluation of FCS rotations
The angle between vessel and FCS, δ, is to be evaluated
along the time series, implementing a model of the sticking/sliding behaviour of the FCS bearings.
The resulting moment at fairlead connection is to be
assessed depending on chain relative angle with fairlead
and line tension, defining two working modes (see Fig 1):
• a sticking mode: when the moment is lower than the
limiting moment, the angle δ remains constant
October 2014
Alternative evaluation of FCS sliding limits
Alternatively, the FCS sliding limits may be evaluated based
on friction tests of the bushing material. The upper bound
value of the static friction coefficient μ of the bearing material with steel is to be assessed in water for submerged FCS
and in air for FCS above water for the range of loads seen in
fatigue mooring simulation time series.
Test shall be conducted to evaluate the performance and suitability of the bearing material for this specific application,
considering low motion and low sliding distance. The test will
be perform with the bearing under sea water condition with
controlled temperature. For each test the following results will
be at least recorded: friction torque, displacement, continuous friction curve, continuous temperature curve.
Bureau Veritas
11
NI 604, Sec 2
Before and after each test, thickness measurement and surface roughness will be recorded for wear assessment. The
rolling effect (if any) shall not be considered for the definition of sliding distance during the test.
M lim = 0,55 μDF
with:
: Instantaneous axial load on the FCS
D
: Diameter of the axis in the bearing.
This limiting moment can be expressed in general as a
break-out angle.
1.2.6
Factory acceptance tests on bushing material
The static friction coefficient of the material from the actual
production of the bushings of the FCS is to be measured for
the tension range evaluated in mooring simulations and
meet the values determined during the prototype tests in
[1.2.4] or in [1.2.5].
2
2.1.1
DDyn
: Fatigue damage obtained through dynamic calculation
DQS
: Fatigue damage obtained through quasi-static
calculation.
Note 1: Definition of quasi-dynamic analyses is provided in
NR493, Sec 3, [2.3].
2.2
2.2.1
Selection of design conditions
Loading conditions
A set of representative configurations of the system is to be
selected for the analyses, so as to cover all intended situations of operation of the Unit and to ensure that the most
onerous configurations have been examined.
The whole range of variation of draft of the units is to be
considered. As a minimum, the following drafts are to be
considered:
Requirements for mooring analysis
2.1
DDAF = DDyn / DQS
with:
The following moment limit Mlim is to be considered:
F
conditions assessed for fatigue estimation. The DDAF, not
being lower than 1, is estimated as following:
• the ballasted draft or the minimum draft in operational
conditions
Mooring Analysis Method
Dynamic analyses
• the maximum draft in operational conditions
Fatigue calculation is to be performed based on time-domain
dynamic mooring analyses with fine representation of vessel
characteristics and behaviour, riser characteristics and behaviour and mooring line characteristics and behaviour. The provision of NR493, Sec 3, [2.4] and NR493, Sec 3, [5.2] are to
be fulfilled.
• an intermediate draft maximizing the unit's rotations,
obtained by scanning the different operational loading
conditions from the unit's loading manual. As a guidance, this draft can be obtained by comparing roll and
pitch natural periods with metocean data on site (wave
peak periods).
Coupling issues between vessel and mooring system are to
be investigated. Dynamic mooring analysis may be limited to
line dynamics when coupling effects are proven negligible.
Additional draft may be considered in order to represent the
whole range of possible loading conditions. Realistic probability of the vessel to be in each condition is to be applied
on fatigue damage in each configuration.
2.1.2
Quasi-dynamic analyses
Quasi-dynamic time-domain analyses may be used as a first
screening method for combined fatigue damage.
The designing environment are then to be reanalyzed
through dynamic analysis. The extent of the environments
to be reanalyzed through dynamic calculations and the
methodology for integrating dynamic results will be evaluated by the Society on a case by case basis depending on
the system and the metocean conditions of the site.
As a minimum for guidance purpose, the following seastates are to be assessed through dynamic analyses:
• the 10 most probable seastates
• the 10 most damaging seastates considering probability
of occurrence, and
• the 10 seastates with highest damage without considering probability of occurrence.
The ratios between fatigue damage estimated through
dynamic analyses and the fatigue damage estimated
through quasi-dynamic analyses, called Damage Dynamic
Amplification Factors DDAF obtained on these seastates are
to be conservatively applied to the whole set of metocean
12
Other relevant conditions with realistic probabilities are to
be assessed, such as operating/ survival conditions with corresponding drafts connected and disconnected conditions
of exporting vessel.
2.2.2
Environment
For a given loading condition, a series of metocean conditions that are representative of the long term conditions of
the intended site and of the operating limits in this condition is to be considered. This set of environmental conditions may be time series obtained by hind-casts data, or
may be derived from available statistical data of waves
(scatter diagrams) combined in an appropriate way with
current and wind data to account for joint probabilities.
For each metocean condition, the fatigue damage is calculated by Rainflow counting and Palmgren-Miner sum on a
the stress time series (see Sec 3, [4]) derived from the mooring analysis on a 3 hour long sea state in order to obtain a
statistically stationary process.
Total damages have to be calculated taking into account the
number of occurrence of the event over the total design life
of the unit.
Bureau Veritas
October 2014
NI 604, Sec 2
2.2.3 Corrosion
The following corrosion allowance of chain has to be considered:
• 0.4mm/year in the splash zone (+/− 110% of the relative
wave elevation at mooring line location with a probability of occurrence of 5% or +/− 5 m around free surface,
whichever greater)
• 0.3mm/year in the remaining length for under water FCS
or fairlead high above the water surface.
ses and the tolerances on fabrication, installations and in
service conditions have to be performed. The most onerous
conditions are to be considered to define the combined
fatigue design damage of the top chain segment.
2.3.2 In addition, the effect of all the simplifications and
linearization used in the mooring analysis models are to be
assessed and demonstrate to provide a Safety Level equivalent to a complete detailed fully coupled dynamic model.
For fatigue assessment, a minimum of half of the corrosion
allowance on the design life of the unit is to be accounted.
2.3.3 As a minimum, the effect of following sensitivities are
to be performed, or justified by proper mean:
Note 1: These corrosion rates seem relevant for cold seas but may
be insufficient in tropical seas. Corrosion rates may be increased
based on site conditions and relevant surveys or Operator's or local
regulation specifications.
• effect on mooring line pretension of the whole range of
tolerances defined in installation specifications
2.3
• effect of tolerances on mooring line components characteristics (stiffness and weight)
Sensitivity on loading conditions and
mooring system model
• effect of tolerances in bearing material on FCS behaviour
2.3.1 Within the set of representative configurations of the
system to be accounted for the fatigue damage evaluation,
sensitivity analyses on the different parameters of the analy-
October 2014
• effect of marine growth additional weight and drag area
obtained from Metocean conditions at the mooring site
• effect of variations of friction coefficient of steel
between links when the fairlead has a sliding limit
higher than the chain links sliding limits.
Bureau Veritas
13
NI 604, Sec 3
SECTION 3
COMBINED FATIGUE ESTIMATION
Symbols
T
: Tension in the line at top chain attachment point
P
: Pretension in the line at top chain attachment
point
α
: Chain angle at connection considering a perfect
ball-and-socket connection
β
: Angle between fairlead and vessel
γ
: Relative chain angle
γTT
: Mean stress correction factor on multiaxial OPB
SCF
αint
: Interlink angle between the considered link and
the next adjacent link
d
: Chain diameter
D
: Total fatigue damage
Di
: Elementary fatigue damage
: Fairlead - Chain stopper
FEM
: Finite Element Methods
1.1.3 The aim of the present section is to present the methodology to evaluate the stress cycle time series based on the
results of the mooring analysis and to recombine them for
the evaluation of combined top chain fatigue damaged.
1.1.4 The methodology to be adopted to define and evaluate the design parameters such as interlink stiffness, stress
concentration factors in the chain link or SN curves from
full scale tests and FEM calculations are also presented in
this Section.
1.1.5 Available design parameters are presented in App 1.
These parameters can be used within their range of applicability without additional full scale tests on chain.
D-DAF : Dynamic Damage Amplification Factor
FCS
1.1.2 The stresses can be linearly decomposed in TT
stresses, OPB stresses and IPB stresses that can be evaluated
separately and recombined by proper means.
1.1.6 In the following part of the document, the “interlink
stiffness” is defined as the range of moment at interlink for a
given tension and a given range of interlink angle.
TT
: Tension-Tension loading
IPB
: In-plane bending of chain
OPB
: Out-of-plane bending of chain
2
MOPB
: Moment in chain at interlink contact area in
OPB direction
2.1
MIPB
: Moment in chain at interlink contact area in IPB
direction
Definition of interlink stiffness
Tests on full scale chains
ΔσTT
: TT stress variation due to tension variation at the
considered hotspot
2.1.1 Full scale tests are to be performed on chains from
the actual manufacturer that will be retained for chain manufacturing.
ΔσOPB
: OPB stress variation due to OPB moment variation at the considered hotspot
Chains are to be in the same diameter as the one used in the
project.
ΔσIPB
: IPB stress variation due to IPB moment variation
at the considered hotspot
Chain configuration in test bench and attachment points in
test bench have to be representative of combined loading
phenomena occurring on the unit on site.
ΔσTT, nom : TT nominal stress variation due to tension variation
ΔσOPB, nom: OPB nominal stress variation due to OPB
moment variation
ΔσIPB, nom : IPB nominal stress variation due to IPB moment
variation.
1
1.1
General
General
1.1.1 Tension and bending cyclic loads are creating stress
cycles in chain. This stress induced by TT, OPB and IPB
loadings is to be estimated through the post processing of
time series from mooring analyses.
14
2.1.2 Tests are to reproduce cycling for different tension and
angular variations in accordance with the range of tension
and relative angles sustained by the unit moored on site.
Due to the hysteresis of the bending moment during a loading range, chain has to sustain a sufficient number of cycles
to assess non-linear bending moments and stresses and their
variability, for each tension and angle variation (see Fig 1).
2.1.3 Chain links in test bench are to be implemented with
measurement device such as but not limited to inclinometers and strain gauges in order to validate and calibrate
results of FEM calculations of stresses.
Testing program specification and test results are to be submitted to the Society for review.
Bureau Veritas
October 2014
NI 604, Sec 3
Note 1: FEM analyses will not be deemed sufficient to assess the
interlink stiffness due to the fact that the material properties and the
effective contact area cannot be modelled accurately. This has been
confirmed by full scale tests and the corresponding FEM calculations have shown unconservative results for the interlink stiffness.
Figure 1 : OPB/IPB Moment hysteresis loop
2.3.3 The coefficient of variation around this best fit law is
to be provided.
3
Evaluation of bending moments
3.1
3.1.1
Bending moment threshold
Friction parameter
The friction coefficient of chain in air generally is between
0,5 and 0,6 and the coefficient of friction in seawater is
between 0,25 and 0,35.
As a basis for design a coefficient of 0,5 in air and 0,3 in
seawater can be considered.
2.2
In case of non-rotating fairlead, or when the fairlead sliding
limit is higher than chain links sliding limits, sensitivity
analyses on friction parameters are to be considered.
Results from other tests
2.2.1 Results from previously performed full scale model
tests on equivalent chain diameters and grade can be used
in order to derive design parameters provided that the tested
tensions and angles are in line with the requirement of the
project.
The results of the tests will be reviewed by the Society on a
case by case basis.
2.2.2 Recognized design parameters can be used for the
combined fatigue assessment, with prior agreement by the
Society.
The test data used to derive these design parameters are to
be documented and the domain of applicability of the
design parameters is to be in line with the requirement of
the project.
3.1.2
Sliding threshold in chain
It has been demonstrated that the same bending stiffness
curve can be used in air and in seawater. However, in seawater, bending moment in chain links are limited in each
link to a sliding threshold where the two links begins to
slide one on the other. This threshold is to be implemented
in interlink stiffness law.
When the sliding threshold is exceeded, the moment
remains constant while the angle is increasing. When the
angle reaches a local extremum, the chain sticks back. This
is creating hysteresis loops of moment versus interlink angle
(see Fig 1).
The sliding threshold Mthreshold is defined as follows:
Mthreshold = μ T d/2
with:
2.2.3 Results from App 1 may be used for chains in R3, R3S
and R4 grade with chain nominal diameter from 84 mm to
146 mm.
Out of this range of chains, these values are to be used with
special care and extrapolation of results will be reviewed by
the Society on a case by case basis.
2.3
: Actual tension
μ
: Friction coefficient
d
: Chain nominal diameter.
3.2
Stiffness variability
3.2.1 The variability on stiffness curve is to be considered
in OPB and IPB stiffness.
Interlink stiffness from full scale tests
2.3.1 Global best-fitted interlink stiffness law and variability around this average law has to be deduced from the testing program for the whole range of tension and angle
variation sustained by the unit on site.
2.3.2 A best fit model of interlink stiffness is to be evaluated
from the results of the tests, providing the interlink moment
as a function of the interlink angle and tension. Fitting
methodology will be reviewed on a case by case basis by
the Society.
October 2014
T
This variability, corresponding to the variability of the contact area after the sliding of one link on the other, is considered as statistically independent of the other parameters of
the stiffness law.
It can thus be represented as an independent variable factoring the stiffness law.
In absence of more detailed statistics of variability based on
larger sets of data, the variability of the stiffness with regards
to best fit stiffness curve can be considered as following a
log normal distribution.
Bureau Veritas
15
NI 604, Sec 3
The shape factor, d, of the distribution of the stiffness variability can be linked to the coefficient of variation (COV) of
the stiffness by the following formula:
ln ( 1 + COV 2 ) = δ
Figure 2 : Example of beam model of chain for
interlink angle estimation
2
where the coefficient of variation is defined by the ratio
between the standard deviation and the mean value of the
stiffness.
As the fatigue damage evaluation corresponds to an integration of the stresses and thus of the moments in the time
domain, this independent variable is equivalent to a constant factor ZS on the stiffness law, only depending on the
shape factor δ and the fatigue SN-curve exponent m.
3.3.3
2
mδ
ln Z S = ---------2
Time series of interlink angles and moments
This factor ZS is to be applied on OPB and IPB stress range
(see [4.3.2]).
The time series of interlink angles/moments is to be
obtained by applying the relation obtained by static beam
analysis on time series of tensions and relative chain angles
at FCS.
3.3
Simplified methodologies are generally not allowed, except
if demonstrated that an equivalent Safety Level is provided.
3.3.1
Static OPB/IPB moments evaluation
Chain interlink angles
The interlink angle between two adjacent links of the top
chain section is only related to chain relative angle with
fairlead and the tension at fairlead by the chain interlink
stiffness.
The interlink angle drops regularly from one link to the next
one in the top chain and interlink angle is negligible after
20 links.
3.3.2
More advanced methodologies will be reviewed on a case
by case basis by the Society, in particular, methodologies
accounting for link stiffness in the mooring analysis.
4
Combined stress estimation
4.1
Stress concentration factor estimation
4.1.1
FEM calculations for stress concentration
factors
Mooring analyses and static OPB/IPB simulations provides
time series of tension loads and interlink moments at contact area.
Implicit formulation between chain tension
and angles and interlink moments
An implicit formulation of the relation between interlink
angles on the first links of the line and fairlead relative angle
and tension can be drawn that is only dependent on the formulation of the interlink stiffness, i.e. of the chain diameter,
grade and manufacturer.
In order to obtain stresses due to TT, OPB and IPB loadings,
stress concentration factors on TT load and OPB interlink
moments and IPB interlink moments are to be evaluated
through FEM calculations. These calculations and their post
processing are to be submitted for review.
This relation is independent of dynamic and memory effects
and can be estimated by static calculations.
4.1.2
This evaluation is to be done through non-linear static finite
element analysis of the first 20 links.
Each link is to be represented as a beam with the same stiffness as a link and the interlink stiffness with bending
moment threshold is to be implemented between the links.
The model is to be loaded with line tension and in plane
and out-of plane relative angles at fairlead combinations
covering the whole range of tension and angles obtained
from the mooring analysis (see Fig 2). The twentieth link of
the model can have pinned boundary conditions.
For each loadcase, interlink angles and moments in plane
and out of the plane of the link are to be evaluated for each
link of the model.
16
Requirements on FEM model
A volumic FEM model of a part of the top chain is to be
built. The software and the type of FEM element used for in
the calculation is to be qualified for elastic-plastic calculations with contacts.
The model of the chain is to consider at least one complete
chain link connected with two half links. A realistic definition of contact behaviours, considering a friction in air for
comparison to full scale tests on chains. Chain geometry is
to be in accordance with the manufacturing data in terms of
chain dimensions and tolerances at the end of heat treatment manufacturing step.
One of the half links are to be fully constrained on the
midlink plan (plane of the welding area see Fig 3). The loading of the model is to be performed by applying tensions
and displacements or tension and moments on the other
half link.
Bureau Veritas
October 2014
NI 604, Sec 3
Figure 3 : Critical hotspot on chain link for combined
fatigue of top chain
Point B near OPB hotspot
maximizing combined unimodal
TT+OPB+IPB fatigue
Point C of multimodal
OPB fatigue
Determination of critical hotspots
As the TT, OPB and IPB hotspot stress are located in different
part of the chain link, the fatigue failure location may vary
depending on the magnitude of each loading. Thus different
stresses at different hotspots have to be assessed in fatigue.
OPB hotspot is spread on a wide area with a slow gradient
in stresses thus different location in OPB hotspot area could
be defined. The point maximizing additional TT loading
effects and IPB effects in this area has to be retained as
fatigue failure location instead of maximum OPB location
in order to maximize combined stress.
Crown
area
Point A at start
of bent area
inner side
Additionally in OPB hotspot area, when approaching interlinks contact area, stresses are not uniaxial anymore and
multiaxiality of stresses is to be addressed by appropriate
multiaxial fatigue methods such as Dang Van criterion. This
defines another critical hotspot location.
Reference point M
at mid-link inner side
Material stress-strain (hardening) law used in the calculation
has to be representative of the effective material properties
in the manufactured chain. Bilinear material laws are not
recommended. Ramberg-Osgood or more advanced hardening laws are to be considered.
4.1.3
4.1.5
As guidance, the following hotspot stresses are generally
identified as the most critical in term of combined loading
(see Fig 1):
• pure TT hotspot hereafter called hotspot A
• uniaxial OPB hotspot maximizing TT, OPB and IPB
effects called hotspot B
Loading of the FEM model
The loading is to be performed for different axial tensions
covering the whole set of possible axial tensions contributing to top chain fatigue and full scale test values.
The interlink angles in the model are to cover the whole set
of possible interlink angles variations on site and in the full
scale test values.
All the loading conditions in full scale tests are to be computed on FEM model. FEM results are to be compared with
the results of the tests.
For each loadcase, the following load sequence is to be performed on the FEM model. The loading is to be performed
on unconstrained chain half-link:
• loading of the model in-line up to Rules proof load
value as defined in NR216, Ch 4, Sec 2
• unloading of the model
• multiaxial OPB hotspot with multiaxiality effects closer
to contact area called hotspot C.
4.1.6
Stress concentration factor definition
Cyclic stresses and corresponding stress concentration factors for the different loadings are defined as follows with d
the un-corroded nominal diameter of chain:
Δσ TT
SCF TT = -------------------Δσ TT, nom
and
Δσ OPB
SCF OPB = ----------------------Δσ OPB, nom
with:
2ΔT
Δσ TT, nom = ----------2πd
• axial loading of the model up to specific line tension
• applying to the model a succession of cycles of angular
displacement or moments.
16ΔM OPB
Δσ OPB, nom = ----------------------3
πd
After proofloading step, the chain dimensions are to be in
line with Rules requirements and manufacturers factual
data.
For studless chain, IPB stresses and corresponding stress
concentration factors is defined as following:
Stresses and displacement are to have reached a stable
behaviour between the cycles at the end of the succession
of angular cycles.
4.1.4
Comparison with test results
Δσ IPB
SCF IPB = --------------------Δσ IPB, nom
with:
2, 33 ΔM IPB
Δσ IPB, nom = ---------------------------3
πd
Results of model tests calculations are to be compared with
the results of full scale tests (measures of load cells, strain
gauges, inclinometers, etc.)
For studlink chain, IPB stresses and corresponding stress
concentration factors is defined as following:
Discrepancies between FEM calculations and test results
have to be justified.
Δσ IPB
SCF IPB = --------------------Δσ IPB, nom
October 2014
Bureau Veritas
17
NI 604, Sec 3
with:
2, 06 ΔM IPB
Δσ IPB, nom = ---------------------------3
πd
proven not conservative. As response period of TT loading,
OPB loadings and IPB loadings are in the same order of
magnitude, statistical damage combination methods are not
applicable for combined fatigue calculation.
These stress concentration factors can be estimated through
adequate FEM calculation calibrated by full scale model
tests on chain.
4.3.2 Stresses are to be combined by proper means, by
summation of time series.
4.2
As the chain link has 2 symmetry planes, four possible location of fatigue crack initiation exists on each side of the link.
Corrosion effect
4.2.1
Nominal stresses modification in chain due to
corrosion
Stress for fatigue damage computation are to be calculated
considering the material loss due to corrosion at mid life of
the unit.
The hypothesis or uniform corrosion can be considered as
valid in the top chain. The effect of a uniformly spread loss
of material on the link can be estimated as an increase of
the TT, OPB and IPB nominal stresses as follows:
2ΔT
= -------------------------2
πd corroded
Δσ OPB, nom
with:
Ld
rcorr
Δσ combined = Z corr ( Δσ TT ± Z S Δσ OPB ± Z S Δσ IPB )
Zcorr
: Defined in [4.2.2]
ZS
: Defined in [3.2.1].
Note 1: Based on our experience, none of the four resulting combined stress can be discarded from the analysis.
16ΔM OPB
-3
= -----------------------πd corroded
Δσ IPB, nom, studless
The combined stress is defined as following with the sign
before OPB and IPB stress range depending on the location
in the link.
where:
L
d corroded = d uncorroded – -----d r corr
2
Δσ TT, nom
Due to the symmetry planes and to the phase difference
between the loadings, the loads in the four locations are
anti-symmetric and combined stresses and fatigue calculation is to be performed in each of the four locations in Fig 4.
Figure 4 : The four anti-symmetrical fatigue
failure location
2, 33 ΔM IPB
= ---------------------------3
πd corroded
: Design life of the unit
: Loss of diameter due to corrosion per year.
4.2.2
Stress concentration factors modification in
chain due to corrosion
When FEM calculations are performed on chains in as-new
conditions, a geometrical corrosion factor is to be applied
on SCF to account to the variation of the chain link geometry due to material loss.
5
Design fatigue damage calculation
For chain reductions at mid design life lower than a 5%
diameter loss, this geometrical corrosion factor Zcorr can be
taken as 1,08, to be multiplied to the SCF for new chain,
accounting for corrosion and manufacturing tolerances.
This factor can be replaced by an evaluation of the SCF on a
chain link with corrosion at mid-life.
5.1
For chain reduction at mid-life higher than a 5% diameter
loss, SCF have to be calculated by proper FEM analyses
based on corroded model with corrosion at mid-life (as per
[4.1.2]).
SN curves in air may be considered, when the FCS is positioned in air far from the splash zone, i.e. higher than:
When the FEM calculations are performed on corroded
models, close attention is to be made on the proofload
applied in order to obtain representative deformations of
the proofloaded chain links. These calculations are to be
submitted to the Society for review.
• 5 meters above free surface, whichever more critical.
4.3
Stresses combination
4.3.1 Fatigue damage calculation is to be performed on
combined stresses. Fatigue calculation by simple summation of fatigue damage from each loading is not allowed as
18
5.1.1
SN-curve
Environmental conditions to be considered
As a general matter for OPB calculations, SN curves for free
corrosion in sea water are to be considered.
• 110% of the relative wave elevation at mooring line
location with a probability of occurrence of 5%
SN curve in sea water with cathodic protection is generally
not to be considered for OPB calculations. Should cathodic
protection be considered in the calculation, a detailed
inspection and maintenance plan with regular verification
of cathodic potential in the 6 first links of the chain is to be
provided for approval.
Calculations in seawater with and without cathodic protection are to be provided in order to define inspection and
maintenance minimum frequency.
Bureau Veritas
October 2014
NI 604, Sec 3
Table 1 : SN curves for combined fatigue calculation
Environmental
Case
First slope
Second slope
log K1
m1
Seawater free corrosion
12,436
3
Seawater under
protection
14,917
4
Air
cathodic
log K2
m2
No second slope
17,146
15,117
Δσ at N = 107
cycles
5
106,97
4
Note 1: Other SN curves may be defined by the designer provided they are documented by a sufficient amount of fatigue tests.
5.1.2 Basis SN curve
The design fatigue SN curves for OPB computations are
defined as follows, with K and m parameter in Tab 1:
m
K = NΔσ combined
Fatigue damage calculation
5.2.1 Fatigue stress cycles for each seastate are to be
obtained by Rainflow counting on combined stress time
series.
Fatigue damage on the seastate is to be obtained by Miner
sum of individual cycle damage. The individual damage for
a single cycle of combined stress di can be computed as following:
m
Δσ combined
d i = -----------------------K
By applying miner sum, the damage on one seastate dss is
thus:
m
d ss =
Δσ combined
 -----------------------K
cycles
The computed total fatigue damage Dtotal during the design
life LD , in years, of the unit on the whole set of seastate with
a probability of occurrence pss of each seastate is obtained
October 2014
D total =

p ss N SY L D d i
SeaStates
Other SN curves may be defined provided they are documented by a sufficient amount of fatigue tests on the actual
steel material from the same chain grade of the same manufacturer. These design SN curves have to be defined with a
survival probability of 97,7% (i.e. mean SN curve minus 2
standard deviation).
5.2
as follows, considering NSY as the number of seastate per
year (equal to 2922 seastates for 3 hour long seastates):
5.3
Design criteria
5.3.1 The design service life is the duration, in years, that
the unit is intended to stay on site. The combined fatigue of
mooring lines top chain is to be assessed for service lives
higher than 2 years when the mooring line pretensions are
higher than 10% of the Minimum breaking strength of a
chain of the same diameter in Oil Rig Quality (ORQ) grade.
5.3.2 The safety factor is defined as the inverse of the maximum combined damage computed on the total service life
of the unit.
5.3.3 The minimum safety factor, for the top chain of each
mooring line, is depending on the maximum slope parameter m of the SN-curve used for fatigue calculation and equal
to:
• 3 for single slope free corrosion SN-curve when m = 3
• 5 for dual slope SN curve when m = 4 or m = 5, such as
typical SN-curves in air and under cathodic protection.
Should part of the sensitivity analyses be omitted or less
advanced computation methods such as frequency domain
simulations be used for damage computation, the minimum
safety factor is 10, with prior agreement by the Society.
Higher safety factors may be applied, if specified by the
unit's operator or local regulations.
Bureau Veritas
19
NI 604, App 1
APPENDIX 1
1
ALTERNATIVE DESIGN REQUIREMENTS
General
1.1
2.1.2 Interlink bending moment and stiffness curve
The interlink bending moment Mi (αint ,T, d), in N.mm, for
both OPB and IPB, can be evaluated using the following
parametric function:
Tension-tension, in-plane bending and
out-of-plane bending modes
1.1.1 The recognized design parameters defined in this
Appendix may be used for the calculation of the combined
fatigue of top chain under tension-tension (TT), in-plane
bending (IPB) and out-of-plane bending (OPB).
This formulation is limited to chain diameters from 84 mm
to 146 mm. Out of this diameter range, the formulation is to
be considered with special care and the approval by the
Society is to be dealt with on a case-by-case basis.
Note 1: This range of diameters is based on the static tests performed during the considered testing programs.
Note 2: This formulation is based on tests on chain grades QR3 to
QR4. The formulations can be extended to higher grades provided
no limitation of the validity of this formulation has been identified
3
P ( α int )  T  a ( Δαi )  d  2a ( Δαi ) + b ( Δαi )
πd
---------- ------------------M i (αi ,T, d) = --------- C -------------------------- 100
16 G + P ( α int )  0,14 d 2
where:
αint
: Interlink angle, in degree
T
: Mooring line tension, in kN
d
: Chain diameter, in mm
C = 354
G = 0,93
P(αint) = αint + 0,307 αint3 + 0,048 αint5
a(αint) = a1 + a2 tanh(a3 αint)
b(αint) = b1 + b2 tanh(b3 αint)
In seawater, the value of Mi (αint ,T, d) is limited by the sliding moment between links (see Sec 3, [3.1.2]).
Note 1: The Best Fit model of interlink moment using least square
method developed in JIP Chain OPB can also be used.
by the industry.
2
Table 1 : Parameters a1, a2, a3, b1, b2 and b3
Evaluation of stresses in mooring line
2.1
2.1.1
OPB and IPB stiffness and moments
a2 = 0,532
a3 = 1,020
b1 = −0,433
b2 = −1,640
b3 = 1,320
2.2
General
A non-linear evaluation of the interlink stiffness between
the links is provided as a relationship between the interlink
angle, the tension in the line and the interlink moment in
OPB and in IPB.
The global moment of the mooring line can be derived from
the interlink stiffness in OPB and IPB, providing the interlink
angle of each link as a function of the tension in the line
and the global angle of the mooring line with regard to the
fairlead. This procedure can be performed by finite element
analyses on beam models as per Sec 3, [3.3].
The OPB and IPB stresses can be derived from the interlink
moments and angles in OPB and IPB for fatigue calculation
as per Sec 3, [4].
OPB and IPB stresses
2.2.1
Stress concentration factors for studless chains
Stress concentration factors (SCF) are based on the formulation given in Sec 3, [4].
For studless chains, the stress concentration factors for locations A (pure TT), B and B' (uniaxial OPB) and C (multiaxial
OPB) are defined in Tab 2.
This stiffness can be considered equal for both OPB and IPB
phenomena, as both OPB and IPB phenomena are symmetrical: one link works under out-of-plane bending mode
when the adjacent one works under in-plane bending
mode.
20
a1 = 0,439
Table 2 : Stress concentration factors
Location
Loading
mode
A
B
B’
C
TT
4,48
2,08
1,65
1,04
OPB
0
1,06
1,15
1,21 γTT
IPB
1,25
0,71
0,66
1,50
Due to multiaxiality of stresses at location C, the mean
stress effect cannot be neglected for OPB loading and a
mean stress correction factor γTT is to be introduced on multiaxial OPB SCF, as follows:
P
γ TT = 1 + 0, 9  ------------ – 0, 15 
 MBL

not being less than 0,95.
Bureau Veritas
October 2014
NI 604, App 1
Where:
P
: Mooring line pretension, in kN
MBL
: Mooring line breaking strength, in kN.
The variability of the stiffness can be considered as a factor
ZS on the interlink moment, taken equal to 1,06 in seawater
free-corrosion and 1,10 in air or under cathodic protection.
For studlink chain, it is recommended to perform a detailed
FEM analysis under TT, OPB and IPB loading modes.
2.2.2
Variability of the stiffness and the stress on
one cycle
The variability of the stiffness curve and thus of the stress,
during an OPB/IPB cycle is to be accounted (see Sec 3,
[3.2]). This stress variability can be modeled as a constant
factor on the interlink stiffness curve, equal to:
2
mδ
Z s = exp  ----------
 2 
where:
m
: Exponent parameter of the SN-curve
δ
: Standard deviation of the ratio between the
measured interlink stiffness and the modeled
one.
October 2014
2.2.3 Effect of the diameter
In order to account for the effect of the material thickness
(chain bar diameter) on the fatigue resistance, the combined
stress cycle is to be factored as follows:
d k
Δσ factored = Δσ combined  --------
 d ref 
where:
d
: Chain diameter, in mm
: Reference chain diameter equal to 84 mm
dref
k
: Thickness exponent equal to 0,15.
2.2.4 S-N curve
When using the methodology in App 1, the following single
slope design SN curve may be used in sea water under free
corrosion instead of values in Sec 3, Tab 1:
• log K = 12,575 and
• m = 3.
Bureau Veritas
21
NI 604, App 1
22
Bureau Veritas
October 2014